Group #14674804 — subgroups

Subgroups — #14674804

Order 2816.

150 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070895	C₂	1	1	yes	maximal, characteristic
2	#13070891	C₂	1	1	yes	maximal, characteristic
3	#13066818	C₂	1	2	yes	maximal
4	#13066816	C₂	1	2	yes	maximal
5	C₁₁×#1397	C₂	1	1	yes	maximal, characteristic
6	#10622296	—	2	1	no	—
7	#10622295	—	2	1	no	—
8	C₂×C₁₁×C₃₂	C₂²	1	2	yes	—
9	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	#10622143	—	2	1	no	—
11	#10622142	—	2	1	no	—
12	#10622142	C₂²	1	2	yes	—
13	#10622142	C₂²	1	1	yes	characteristic
14	#10622142	C₂²	1	1	yes	characteristic
15	#66923	—	4	1	no	—
16	#66922	—	4	1	no	—
17	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
18	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
19	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
20	#66882	—	2	2	no	—
21	#66882	—	2	1	no	—
22	#66882	—	2	1	no	—
23	#66882	—	4	1	no	—
24	#66881	—	4	1	no	—
25	C₁₁×C₃₂	Q₈	1	4	yes	complemented
26	#13734	—	11	1	no	maximal, Sylow
27	C₂×Dic₂₂	—	8	1	no	—
28	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
29	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
30	C₄²×C₁₁	D₈	1	1	yes	characteristic
31	C₄⋊Dic₁₁	—	4	1	no	—
32	C₄⋊Dic₁₁	—	4	1	no	—
33	C₄⋊Dic₁₁	—	4	2	no	—
34	C₄⋊Dic₁₁	—	8	1	no	—
35	Dic₁₁⋊C₄	—	8	1	no	—
36	Dic₁₁⋊C₄	—	8	1	no	—
37	C₁₁×C₁₆	Q₁₆	1	2	yes	—
38	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
39	#2253	—	11	1	no	—
40	#2252	—	11	1	no	—
41	#1424	—	11	2	no	—
42	#1423	—	11	2	no	—
43	#1397	D₁₁	1	1	yes	characteristic
44	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
45	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
46	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
47	C₂×Dic₁₁	—	8	1	no	—
48	C₂×Dic₁₁	—	8	1	no	—
49	C₂×Dic₁₁	—	8	2	no	—
50	Dic₂₂	—	16	2	no	—
51	C₈×C₁₁	Q₃₂	1	2	yes	—
52	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
53	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
54	#500	—	22	1	no	—
55	#499	—	22	1	no	—
56	C₂×C₃₂	C₂×D₁₁	1	2	yes	—
57	#367	—	22	1	no	—
58	#366	—	11	1	no	—
59	#366	—	11	2	no	—
60	#366	—	11	1	no	—
61	#366	—	22	1	no	—
62	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
63	C₂²×C₁₁	C₂×D₁₆	1	1	yes	characteristic
64	C₄×C₁₁	—	2	1	no	—
65	C₄×C₁₁	—	2	1	no	—
66	C₄×C₁₁	#500	1	1	yes	characteristic
67	C₄×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
68	Dic₁₁	—	16	2	no	—
69	Dic₁₁	—	16	1	no	—
70	Dic₁₁	—	16	1	no	—
71	C₄⋊Q₈	—	44	1	no	—
72	#125	—	44	1	no	—
73	C₂×C₁₆	D₄₄	1	1	yes	characteristic
74	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
75	#107	—	22	2	no	—
76	#107	—	22	1	no	—
77	#107	—	22	1	no	—
78	#107	—	44	1	no	—
79	#106	—	44	1	no	—
80	C₄×C₈	D₄₄	1	1	yes	characteristic
81	C₃₂	Dic₂₂	1	4	yes	complemented
82	C₂×C₁₁	#2252	1	1	yes	characteristic
83	C₂×C₁₁	#2263	1	1	yes	characteristic
84	C₂×C₁₁	#2264	1	1	yes	characteristic
85	C₂×Q₈	—	88	1	no	—
86	C₂×C₈	D₈₈	1	1	yes	characteristic
87	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
88	C₄⋊C₄	—	44	1	no	—
89	C₄⋊C₄	—	44	1	no	—
90	C₄⋊C₄	—	44	2	no	—
91	C₄⋊C₄	—	88	1	no	—
92	C₄⋊C₄	—	88	1	no	—
93	C₄⋊C₄	—	88	1	no	—
94	C₄²	D₈₈	1	1	yes	characteristic
95	C₁₆	Dic₄₄	1	2	yes	—
96	C₁₆	C₂×Dic₂₂	1	2	yes	—
97	C₁₁	#13734	1	1	yes	characteristic, complemented, Sylow
98	Q₈	—	176	2	no	—
99	C₂×C₄	—	88	1	no	—
100	C₂×C₄	—	88	1	no	—
101	C₂×C₄	—	88	2	no	—
102	C₂×C₄	D₁₇₆	1	1	yes	characteristic
103	C₂×C₄	D₁₇₆	1	1	yes	characteristic
104	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
105	C₈	Dic₈₈	1	2	yes	—
106	C₈	#66922	1	1	yes	characteristic
107	C₈	C₂×Dic₄₄	1	1	yes	characteristic
108	C₂²	C₂×D₁₇₆	1	1	yes	characteristic
109	C₄	—	2	1	no	—
110	C₄	—	2	1	no	—
111	C₄	—	176	2	no	—
112	C₄	—	176	1	no	—
113	C₄	—	176	1	no	—
114	C₄	#10622295	1	1	yes	characteristic
115	C₄	C₂×Dic₈₈	1	1	yes	characteristic
116	C₂	#13070891	1	1	yes	characteristic
117	C₂	#13070931	1	1	yes	characteristic
118	C₂	#13070936	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13070895

C₂

yes

maximal, characteristic

#13070891

C₂

yes

maximal, characteristic

#13066818

C₂

yes

maximal

#13066816

C₂

yes

maximal

C₁₁×#1397

C₂

yes

maximal, characteristic

#10622296

—

#10622295

—

C₂×C₁₁×C₃₂

C₂²

yes

—

C₄×C₁₁×C₁₆

C₂²

yes

—

—

C₂²

yes

—

#10622142

C₂²

yes

characteristic

#10622142

C₂²

yes

characteristic

#66923

—

#66922

—

C₂×C₁₁×C₁₆

D₄

yes

characteristic

C₂×C₁₁×C₁₆

C₂³

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

—

—

—

—

—

C₁₁×C₃₂

Q₈

yes

complemented

#13734

—

maximal, Sylow

C₂×Dic₂₂

—

C₂×C₈×C₁₁

D₈

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

D₈

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

Dic₁₁⋊C₄

—

C₁₁×C₁₆

Q₁₆

yes

—

C₁₁×C₁₆

C₂×Q₈

yes

—

—

—

—

—

D₁₁

yes

characteristic

C₂×C₄×C₁₁

D₁₆

yes

characteristic

C₂×C₄×C₁₁

D₁₆

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

C₈×C₁₁

Q₃₂

yes

—

C₈×C₁₁

C₄⋊Q₈

yes

characteristic

C₈×C₁₁

C₂×Q₁₆

yes

characteristic

#500

—

#499

—

C₂×C₃₂

C₂×D₁₁

yes

—

—

—

—

—

—

C₄×C₁₆

C₂×D₁₁

yes

characteristic

C₂²×C₁₁

C₂×D₁₆

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#500

yes

characteristic

C₄×C₁₁

C₂×Q₃₂

yes

characteristic

Dic₁₁

—

Dic₁₁

—

Dic₁₁

—

C₄⋊Q₈

—

#125

—

C₂×C₁₆

D₄₄

yes

characteristic

C₂×C₁₆

C₂²×D₁₁

yes

—

—

—

—

—

C₄×C₈

D₄₄

yes

characteristic

C₃₂

Dic₂₂

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×Q₈

—

C₂×C₈

D₈₈

yes

characteristic

C₂×C₈

C₂×D₄₄

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₈₈

yes

characteristic

C₁₆

Dic₄₄

yes

—

C₁₆

C₂×Dic₂₂

yes

—

C₁₁

#13734

yes

characteristic, complemented, Sylow

Q₈

—

176

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

D₁₇₆

yes

characteristic

103

C₂×C₄

D₁₇₆

yes

characteristic

104

C₂×C₄

C₂×D₈₈

yes

characteristic

105

C₈

Dic₈₈

yes

—

106

C₈

#66922

yes

characteristic

107

C₈

C₂×Dic₄₄

yes

characteristic

108

C₂²

C₂×D₁₇₆

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

176

—

112

C₄

—

176

—

113

C₄

—

176

—

114

C₄

#10622295

yes

characteristic

115

C₄

C₂×Dic₈₈

yes

characteristic

116

C₂

#13070891

yes

characteristic

117

C₂

#13070931

yes

characteristic

118

C₂

#13070936

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₇₆
commutator, cosocle	C₂×C₁₁×C₁₆	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₁₁×#1397	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₁₆
hypercenter	#1397	D₁₁
hypocenter	C₁₁	#13734
LCS	G ▷ C₂×C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

subgroup

G/H

center

C₂²

C₂×D₁₇₆

commutator, cosocle

C₂×C₁₁×C₁₆

C₂³

Frattini

C₂×C₁₆

C₂²×D₁₁

Fitting

C₁₁×#1397

C₂

socle, prime radical

C₂²×C₁₁

C₂×D₁₆

D₁₁

C₁₁

G ▷ C₂×C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

N	H ≅ G/N	type
25. C₁₁×C₃₂	Q₈	semidirect
81. C₃₂	Dic₂₂	semidirect
97. C₁₁	#13734	semidirect

H ≅ G/N

type

25. C₁₁×C₃₂

Q₈

semidirect

81. C₃₂

Dic₂₂

semidirect

97. C₁₁

#13734

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13070895	2
#13070891	2
#13066818	2
#13066816	2
C₁₁×#1397	2
#13734	11

subgroup

index

C₁₁×#1397

Subgroups — #14674804

Conjugacy classes of subgroups

Complements

Maximal subgroups